Question

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 1 out of 3
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Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation 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.
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 a more standard form)

Distribute $\frac{3}{4}$ on the right - hand side: $y-5=\frac{3}{4}x+3$
Add 5 to both sides of the equation: $y=\frac{3}{4}x+3 + 5$
Simplify the constants: $y=\frac{3}{4}x+8$
We can also write it in standard form $Ax+By = C$. Multiply through by 4 to get rid of the fraction:
$4y=3x + 32$
Then, $3x-4y=-32$ or $y-\frac{3}{4}x = 8$ (but slope - intercept form $y=\frac{3}{4}x + 8$ is also correct)

Answer:

The equation of the line is $y=\frac{3}{4}x + 8$ (or in standard form $3x-4y=-32$)