Question

score: 7/10. penalty: 0.5 off
question
what is the equation of the line that passes through the point (-4, 5) and has a slope of \\(\frac{3}{4}\\)?
answer attempt 2 out of 3
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Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1=-4$, $y_1 = 5$ and $m=\frac{3}{4}$.

Step2: Substitute values into point - slope form

Substitute $x_1=-4$, $y_1 = 5$ and $m=\frac{3}{4}$ into the point - slope form:
$y - 5=\frac{3}{4}(x-(-4))$
Simplify the right - hand side: $y - 5=\frac{3}{4}(x + 4)$

Step3: Convert to slope - intercept form (optional, but to get the equation in a more familiar form)

Distribute the $\frac{3}{4}$ on the right - hand side:
$y-5=\frac{3}{4}x+\frac{3}{4}\times4$
$\frac{3}{4}\times4 = 3$, so $y-5=\frac{3}{4}x + 3$
Add 5 to both sides of the equation:
$y=\frac{3}{4}x+3 + 5$
$y=\frac{3}{4}x+8$
We can also leave it in point - slope form: $y - 5=\frac{3}{4}(x + 4)$ or convert it to standard form $3x-4y=-32$ (by multiplying both sides of $y=\frac{3}{4}x + 8$ by 4: $4y = 3x+32$, then $3x-4y=-32$)

Answer:

The equation of the line can be written in slope - intercept form as $y=\frac{3}{4}x + 8$, in point - slope form as $y - 5=\frac{3}{4}(x + 4)$ or in standard form as $3x-4y=-32$. (Commonly, slope - intercept form is a common answer, so $y=\frac{3}{4}x + 8$)