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 y-intercept (b) is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at (0, 3). So, \( b = 3 \).

Step2: Calculate the slope (m)

We can use two points on the line. Let's take (0, 3) and (1, 7) (we can see from the graph that when x increases by 1, y increases by 4? Wait, no, wait. Wait, looking at the graph, when x=0, y=3; when x=1, y=7? Wait, no, maybe another point. Wait, actually, let's check the grid. Wait, the line passes through (0, 3) and maybe ( -0.5, 0)? Wait, no, better to use two clear points. Wait, when x=0, y=3; when x=1, what's y? Wait, the line is steep. Wait, maybe (0, 3) and (1, 7)? Wait, no, let's calculate the slope. The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points: (0, 3) and (1, 7)? Wait, no, when x=0, y=3; when x=1, y=7? Wait, the difference in y is 7 - 3 = 4, difference in x is 1 - 0 = 1, so slope is 4? Wait, no, that seems too steep. Wait, maybe I made a mistake. Wait, looking at the graph, when x=0, y=3; when x=1, y=7? Wait, no, maybe the line passes through (0, 3) and (1, 7)? Wait, but let's check another point. Wait, when x=-1, what's y? If x=-1, then from the graph, the line is at y=-1? Wait, no, maybe I misread. Wait, let's take (0, 3) and (1, 7). Then slope \( m = \frac{7 - 3}{1 - 0} = \frac{4}{1} = 4 \)? Wait, no, that can't be. Wait, maybe (0, 3) and (1, 7) is correct. Wait, the line is very steep. Wait, let's confirm. The slope-intercept form is \( y = mx + b \). If b=3, and when x=1, y=7, then 7 = m(1) + 3, so m=4. So slope is 4.

Step3: Write the equation

Using slope-intercept form \( y = mx + b \), where m=4 and b=3, the equation is \( y = 4x + 3 \). Wait, but let's check another point. If x= -0.5, then y = 4*(-0.5) + 3 = -2 + 3 = 1. Looking at the graph, when x=-0.5, y=1? Yes, that seems to match. So the slope is 4.

Answer:

\( y = 4x + 3 \)