andy wrote the equation of a line that has a slope of $\frac{3}{4}$ and passes through the point $(3, -2)$…
andy wrote the equation of a line that has a slope of $\frac{3}{4}$ and passes through the point $(3, -2)$ in function notation. step 1: $y - (-2)=\frac{3}{4}(x - 3)$ step 2: $y + 2=\frac{3}{4}x-\frac{9}{4}$ step 3: $y + 2+2=\frac{3}{4}x-\frac{9}{4}+2$ step 4: $y=\frac{3}{4}x-\frac{1}{4}$ step 5: $f(x)=\frac{3}{4}x-\frac{1}{4}$ analyze each step to identify if andy made an error. yes, he made an error in step 1. he switched the $x$ and $y$ values. yes, he made an error in step 2. he did not distribute $\frac{3}{4}$ properly. yes, he made an error in step 3. he should have subtracted 2 from both sides. no, his work is correct.
Answer
Explanation:
Step1: Check Step 1
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. Given $m = \frac{3}{4}$ and the point $(3,-2)$, we have $y-(-2)=\frac{3}{4}(x - 3)$, which is correct.
Step2: Check Step 2
Distribute $\frac{3}{4}$ in $\frac{3}{4}(x - 3)$: $\frac{3}{4}(x - 3)=\frac{3}{4}x-\frac{9}{4}$, then $y + 2=\frac{3}{4}x-\frac{9}{4}$, which is correct.
Step3: Check Step 3
To isolate $y$, we add 2 to both sides of the equation $y + 2=\frac{3}{4}x-\frac{9}{4}$. The operation $y + 2+2=\frac{3}{4}x-\frac{9}{4}+2$ is correct.
Step4: Check Step 4
Simplify the right - hand side: $\frac{3}{4}x-\frac{9}{4}+2=\frac{3}{4}x-\frac{9}{4}+\frac{8}{4}=\frac{3}{4}x-\frac{1}{4}$, and $y=\frac{3}{4}x-\frac{1}{4}$, which is correct.
Step5: Check Step 5
In function notation, $y = f(x)$, so $f(x)=\frac{3}{4}x-\frac{1}{4}$, which is correct.
Answer:
No, his work is correct.