Question

1. write the equation of a line with slope 4 that passes through the point (3.5, 5) in slope - intercept form.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m = 4$, $x_1=3.5$, and $y_1 = 5$.
Substitute these values into the point - slope formula: $y - 5=4(x - 3.5)$

Step2: Expand the right - hand side

Using the distributive property $a(b - c)=ab - ac$, we have $y - 5=4x-4\times3.5$.
Calculate $4\times3.5 = 14$, so the equation becomes $y - 5=4x - 14$.

Step3: Solve for y (slope - intercept form $y=mx + b$)

Add 5 to both sides of the equation: $y=4x-14 + 5$.
Simplify $-14 + 5=-9$. So the equation is $y = 4x-9$.

Answer:

$y = 4x-9$