5.8.1: Exercises

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For the following exercises, find the $x$- and $y$-intercepts on the graph.

Exercise $\PageIndex{1}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 6 to 6, in increments of 1. The line passes through the points, (negative 2, 5), (0, 3), (3, 0), and (6, negative 3). Note: all values are approximate.$

Exercise $\PageIndex{2}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 6 to 6, in increments of 1. The line passes through the points, (negative 6, 4), (negative 2, 0), (0, negative 2), and (4, negative 6). Note: all values are approximate.$

Exercise $\PageIndex{3}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 6 to 6, in increments of 1. The line passes through the points, (negative 1, negative 6), (0, negative 5), (5, 0), and (6, 1). Note: all values are approximate.$

Exercise $\PageIndex{4}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 6 to 6, in increments of 1. The line passes through the points, (negative 3, negative 6), (0, 0), and (3, 6). Note: all values are approximate.$

For the following exercises, graph using the intercepts.

Exercise $\PageIndex{5}$

$- x + 4y = 8$

Exercise $\PageIndex{6}$

$x + y = - 3$

Exercise $\PageIndex{7}$

$4x + y = 4$

Exercise $\PageIndex{8}$

$3x - y = - 6$

Exercise $\PageIndex{9}$

$2x + 4y = 12$

Exercise $\PageIndex{10}$

$2x - 5y = - 20$

Exercise $\PageIndex{11}$

$y = - 2x$

Exercise $\PageIndex{12}$

$y = x$

For the following exercises, find the slope of the line.

Exercise $\PageIndex{13}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 8 to 8, in increments of 1. The line passes through the points, (negative 5, negative 6), (0, negative 4), and (5, negative 2). Note: all values are approximate.$

Exercise $\PageIndex{14}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 8 to 8, in increments of 1. The line passes through the points, (negative 4, negative 6), (0, negative 1), and (7.2, 8). Note: all values are approximate.$

Exercise $\PageIndex{15}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 8 to 8, in increments of 1. The line passes through the points, (negative 2, negative 8), (0, negative 5), (4, 1), and (8, 7). Note: all values are approximate.$

Exercise $\PageIndex{16}$

Exercise $\PageIndex{17}$

Exercise $\PageIndex{18}$

Exercise $\PageIndex{19}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 8 to 8, in increments of 1. The line passes through the points, (negative 3, negative 7), (0, negative 2), (1, 0), and (6, 8). Note: all values are approximate.$

Exercise $\PageIndex{20}$

$A line is plotted on an x y coordinate plane. The x and y axes range from negative 8 to 8, in increments of 1. The line passes through the points, (negative 6, 4), (0, 2), and (6, 0). Note: all values are approximate.$

For the following exercises, use the slope formula to find the slope of the line between each pair of points.

Exercise $\PageIndex{21}$

(2, 5), (4, 0)

Exercise $\PageIndex{22}$

(−3, 3), (4, −5)

Exercise $\PageIndex{23}$

(−1, −2), (2, 5)

Exercise $\PageIndex{24}$

(4, −5), (1, −2)

For the following exercises, identify the slope and $y$-intercept of each line.

Exercise $\PageIndex{25}$

$y = - 7x + 3$

Exercise $\PageIndex{26}$

$y = 4x - 10$

Exercise $\PageIndex{27}$

$3x + y = 5$

Exercise $\PageIndex{28}$

$4x + y = 8$

Exercise $\PageIndex{29}$

$6x + 4y = 12$

Exercise $\PageIndex{30}$

$8x + 3y = 12$

Exercise $\PageIndex{31}$

$5x - 2y = 6$

Exercise $\PageIndex{32}$

$7x - 3y = 9$

For the following exercises, graph the line of each equation using its slope and $y$-intercept.

Exercise $\PageIndex{33}$

$y = 3x - 1$

Exercise $\PageIndex{34}$

$y = 2x - 3$

Exercise $\PageIndex{35}$

$y = - x + 3$

Exercise $\PageIndex{36}$

$y = - x - 4$

Exercise $\PageIndex{37}$

$y = - 2x - 3$

Exercise $\PageIndex{38}$

$y = - 3x + 2$

Exercise $\PageIndex{39}$

$3x - 2y = 4$

Exercise $\PageIndex{40}$

$3x - 4y = 8$

For the following exercises, find the slope of each line and graph.

Exercise $\PageIndex{41}$

$y = 3$

Exercise $\PageIndex{42}$

$y = - 2$

Exercise $\PageIndex{43}$

$x = - 5$

Exercise $\PageIndex{44}$

$x = 4$

For the following exercises, graph and interpret applications of slope-intercept.
The equation $P = 31 + 1.75w$ models the relation between the amount of Tuyet’s monthly water bill payment, $P$, in dollars, and the number of units of water, $w$, used.

Exercise $\PageIndex{45}$

Find Tuyet’s payment for a month when 0 units of water are used.

Exercise $\PageIndex{46}$

Find Tuyet’s payment for a month when 12 units of water are used.

Exercise $\PageIndex{47}$

Interpret the slope and $P$-intercept of the equation.

Exercise $\PageIndex{48}$

Graph the equation.

For the following exercises, graph and interpret applications of slope-intercept.
Bruce drives his car for his job. The equation $R = 0.575m + 42$ models the relation between the amount in dollars, $R$, that he is reimbursed and the number of miles, $m$, he drives in one day.

Exercise $\PageIndex{49}$

Find the amount Bruce is reimbursed on a day when he drives 0 miles.

Exercise $\PageIndex{50}$

Find the amount Bruce is reimbursed on a day when he drives 220 miles.

Exercise $\PageIndex{51}$

Interpret the slope and $R$-intercept of the equation.

Exercise $\PageIndex{52}$

Graph the equation.

For the following exercises, graph and interpret applications of slope-intercept.
Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation $S = 400 + 0.15c$ models the relation between her weekly salary, $S$, in dollars and the amount of her sales, $c$, in dollars.

Exercise $\PageIndex{53}$

Find Cherie’s salary for a week when her sales were $0.

Exercise $\PageIndex{54}$

Find Cherie’s salary for a week when her sales were $3,600.

Exercise $\PageIndex{55}$

Interpret the slope and $S$-intercept of the equation.

Exercise $\PageIndex{56}$

Graph the equation.

For the following exercises, graph and interpret applications of slope-intercept.
Costa is planning a lunch banquet. The equation $C = 450 + 28g$ models the relation between the cost in dollars, $C$, of the banquet and the number of guests, $g$.

Exercise $\PageIndex{57}$

Find the cost if the number of guests is 40.

Exercise $\PageIndex{58}$

Find the cost if the number of guests is 80.

Exercise $\PageIndex{59}$

Interpret the slope and $C$-intercept of the equation.

Exercise $\PageIndex{60}$

Graph the equation.

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