Question

a line passes through the point (-4, 4) and has a slope of \\(\frac{5}{2}\\). write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. We know that $x_1=-4$, $y_1 = 4$ and $m=\frac{5}{2}$. Substitute these values into the point - slope form:
$y - 4=\frac{5}{2}(x - (-4))$ which simplifies to $y - 4=\frac{5}{2}(x + 4)$

Step2: Convert to slope - intercept form

Slope - intercept form is $y=mx + b$. We need to solve the equation from Step 1 for $y$.
First, distribute $\frac{5}{2}$ on the right - hand side:
$y-4=\frac{5}{2}x+\frac{5}{2}\times4$
$\frac{5}{2}\times4 = 10$, so the equation becomes $y - 4=\frac{5}{2}x+10$
Then, add 4 to both sides of the equation to solve for $y$:
$y=\frac{5}{2}x+10 + 4$
$10 + 4=14$, so $y=\frac{5}{2}x+14$

Answer:

$y=\frac{5}{2}x + 14$