Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, -60), so the y-intercept \( b = -60 \).

Step2: Calculate the slope

Choose two points on the line, e.g., (0, -60) and (80, -10). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-10 - (-60)}{80 - 0} = \frac{50}{80} = \frac{5}{8} \). Wait, no, wait, looking at the graph again, when x=80, y is -10? Wait, no, the line goes through (80, -10)? Wait, no, the right end is at (80, -10)? Wait, no, the graph: when x=80, y is -10? Wait, no, the line is rising? Wait, no, the red line: from (0, -60) to (80, -10)? Wait, no, let's check again. Wait, the grid: each square is 10 units. So from (0, -60) to (80, -10): the change in y is (-10) - (-60) = 50, change in x is 80 - 0 = 80, so slope is 50/80 = 5/8? Wait, but maybe another point. Wait, or (0, -60) and (16, -50)? No, maybe I made a mistake. Wait, the line: when x=80, y is -10? Wait, no, the arrow at x=80 is at y=-10? Wait, the graph shows the line going from the bottom left (like x=-80, y=-90?) to (80, -10)? Wait, no, let's look at the y-intercept: it's at (0, -60). Then, when x increases by 80 (from 0 to 80), y increases by how much? From y=-60 to y=-10: that's an increase of 50. So slope m = 50/80 = 5/8. Wait, but maybe the slope is 5/8? Wait, no, wait, maybe I messed up the direction. Wait, the line is going from (0, -60) to (80, -10): so y goes from -60 to -10, which is +50, x from 0 to 80, +80. So slope is 50/80 = 5/8. Then the slope-intercept form is \( y = mx + b \), so \( y = \frac{5}{8}x - 60 \)? Wait, no, that can't be. Wait, maybe I got the y-intercept wrong. Wait, the line crosses the y-axis at (0, -60), so b=-60. Then, let's take another point: when x=80, y=-10. So plug into y = mx -60: -10 = m80 -60 → 80m = 50 → m = 50/80 = 5/8. So the equation is \( y = \frac{5}{8}x - 60 \)? Wait, but that seems off. Wait, maybe I made a mistake in the points. Wait, maybe the line is (0, -60) and (80, -10): yes, that's correct. So slope is 5/8, y-intercept -60. So the equation is \( y = \frac{5}{8}x - 60 \)? Wait, but let's check with x=0: y=-60, correct. x=80: (5/8)80 -60 = 50 -60 = -10, correct. So that's the equation.

Wait, but maybe I misread the graph. Let me check again. The y-axis: at x=0, the line is at y=-60. Then, moving to the right, at x=80, y is at -10. So the slope is ( -10 - (-60) ) / (80 - 0 ) = 50/80 = 5/8. So the slope-intercept form is \( y = \frac{5}{8}x - 60 \).

Answer:

\( y = \frac{5}{8}x - 60 \)