Question

1. $y = -\frac{5}{2}x + 4$

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=4$. So the y-intercept is the point $(0, 4)$.

Step2: Use slope to find second point

Slope $m=-\frac{5}{2}$, meaning $\frac{\text{change in } y}{\text{change in } x}=-\frac{5}{2}$. From $(0,4)$, move 2 units right (x increases by 2) and 5 units down (y decreases by 5):
$x=0+2=2$, $y=4-5=-1$. This gives the point $(2, -1)$.

Step3: Plot points and draw line

Plot $(0, 4)$ and $(2, -1)$, then draw a straight line through them. Extend the line to cover the grid.

Answer:

The line $y=-\frac{5}{2}x+4$ is graphed by plotting the points $(0, 4)$ and $(2, -1)$ and drawing a straight line through them, extending across the provided coordinate grid.