Question

1. write an equation in slope - intercept form that passes through the points (6, 3) and (5, - 4)
2. write standard form.
3. state the x and y intercepts of the graph of the equation. 2x - 6y=-12
4. graph the given intercepts. x - intercept: - 4 y - intercept: 5
5. graph the equation. x=-5

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,3)$ and $(x_2,y_2)=(5, - 4)$. Then $m=\frac{-4 - 3}{5 - 6}=\frac{-7}{-1}=7$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and one of the points, say $(6,3)$. Substitute $x = 6$, $y = 3$ and $m = 7$ into $y=mx + b$. We get $3=7\times6 + b$, which simplifies to $3 = 42+b$. Solving for $b$ gives $b=3 - 42=-39$.

Step3: Write the slope - intercept form

The equation in slope - intercept form is $y = 7x-39$.

for question 12:
The slope - intercept form $y = 7x-39$ can be rewritten in standard form $Ax+By = C$. Rearranging gives $-7x+y=-39$, or $7x - y=39$.

for question 13:
For the x - intercept, set $y = 0$ in the equation $2x-6y=-12$. Then $2x=-12$, so $x=-6$.
For the y - intercept, set $x = 0$ in the equation $2x-6y=-12$. Then $-6y=-12$, so $y = 2$.

for question 14:
The x - intercept is the point $(-4,0)$ and the y - intercept is the point $(0,5)$. Plot these two points on the coordinate plane and draw a straight line passing through them.

Answer:

$y = 7x-39$