Question

what is the equation in slope - intercept form of the line that passes through the point (-6, 3) and has a slope of \\(\frac{5}{3}\\)? \\(\boldsymbol{a}\\) \\(y = \frac{5}{3}x - 7\\) \\(\boldsymbol{b}\\) \\(y = \frac{5}{3}x + 13\\) \\(\boldsymbol{c}\\) \\(y = \frac{5}{3}x - 11\\) \\(\boldsymbol{d}\\) \\(y = \frac{5}{3}x - 1\\)

Explanation:

Step1: Recall slope-intercept form

Slope-intercept form is $y = mx + b$, where $m$ is slope, $b$ is y-intercept.
We know $m = \frac{5}{3}$, so $y = \frac{5}{3}x + b$.

Step2: Substitute point (-6,3)

Plug $x=-6$, $y=3$ into the equation:
$3 = \frac{5}{3}(-6) + b$

Step3: Calculate $\frac{5}{3}(-6)$

$\frac{5}{3}(-6) = 5\times(-2) = -10$
Equation becomes: $3 = -10 + b$

Step4: Solve for $b$

$b = 3 + 10 = 13$

Step5: Write final equation

Substitute $b=13$ back into $y = \frac{5}{3}x + b$:
$y = \frac{5}{3}x + 13$

Answer:

B. $y = \frac{5}{3}x + 13$