Question

unit 9 #3 - graph equations in point - slope form
identify the point and slope in the given equation, then graph the equation.
1.
equation: $y + 2=\frac{1}{3}(x + 1)$
slope:
point:
2.
equation: $y + 1 = 2(x - 3)$
slope:
point:
3.
equation: $y - 3=-2(x - 4)$
slope:
point:
4.
equation: $y - 5 = 3x$
slope:
point:
5.
equation: $y + 3 = 0(x - 3)$
slope:
point:
6.
equation: $y - 1=-\frac{5}{2}(x + 2)$
slope:
point:

Explanation:

Problem 4:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. We can rewrite the given equation $y - 5 = 3x$ in the form $y - 5=3(x - 0)$.

Step2: Identify slope and point

By comparing with $y - y_1=m(x - x_1)$, we see that the slope $m = 3$ and the point $(x_1,y_1)=(0,5)$.

Step1: Recall point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. The given equation is $y + 3=0(x - 3)$, which can be written as $y-(-3)=0(x - 3)$.

Step2: Identify slope and point

Comparing with $y - y_1=m(x - x_1)$, the slope $m = 0$ and the point $(x_1,y_1)=(3,-3)$.

Step1: Recall point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. The given equation is $y - 1=-\frac{5}{2}(x + 2)$, which can be rewritten as $y - 1=-\frac{5}{2}(x-(-2))$.

Step2: Identify slope and point

By comparing with $y - y_1=m(x - x_1)$, the slope $m=-\frac{5}{2}$ and the point $(x_1,y_1)=(-2,1)$.

Answer:

Slope: $3$, Point: $(0,5)$

Problem 5: