Question

write the equation of the line.
y = -3/5x - 2
y = -5/3x - 2
y = 5/3x - 2
y = 3/5x - 2

Explanation:

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Determine the y - intercept

From the graph, the line crosses the y - axis at $y=-2$, so $b = - 2$.

Step3: Calculate the slope

The slope $m=\frac{\text{rise}}{\text{run}}$. If we choose two points on the line, say the y - intercept $(0,-2)$ and another point, and count the rise and run. The line is increasing (going up from left to right), so the slope is positive. By counting the grid squares, for a run of 5 units to the right, the rise is 3 units up. So $m=\frac{3}{5}$.

Step4: Write the equation

Substitute $m = \frac{3}{5}$ and $b=-2$ into $y=mx + b$, we get $y=\frac{3}{5}x-2$.

Answer:

$y=\frac{3}{5}x - 2$ (the blue - colored option)