Question

1. line 1: (-2,1), (1,-1)

line 2: (1,3), (4,1)
pick the right answer from the possible selections on your screen in eduphoria.

1. graph y = -3x - 1. (g2b)

graph the line on eduphoria

1. write an equation in slope - intercept form of the line that passes through (-1,3) and is parallel to y = 4x - 2.

pick the right answer from the possible selections on your screen in eduphoria.

1. write an equation in slope - intercept form of the line that passes through (0,2) and is perpendicular to y = 1/2x + 1.

pick the right answer from the possible selections on your screen in eduphoria.

Explanation:

6.

Step1: Find slope of Line 1

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For line 1 with points $(-2,1)$ and $(1,-1)$, $m_1=\frac{-1 - 1}{1-(-2)}=\frac{-2}{3}=-\frac{2}{3}$.

Step2: Find slope of Line 2

For line 2 with points $(1,3)$ and $(4,1)$, $m_2=\frac{1 - 3}{4 - 1}=\frac{-2}{3}=-\frac{2}{3}$. Since $m_1 = m_2$, the lines are parallel. But without the options, we can't pick the exact answer from Eduphoria.

7.

Step1: Find y - intercept

For the equation $y=-3x - 1$, the y - intercept $b=-1$, so the line crosses the y - axis at the point $(0,-1)$.

Step2: Use slope to find another point

The slope $m=-3=\frac{\Delta y}{\Delta x}$. Starting from $(0,-1)$, if $\Delta x = 1$, then $\Delta y=-3$. So another point is $(1,-4)$. Plot the points $(0,-1)$ and $(1,-4)$ and draw a straight line through them on Eduphoria.

8.

Step1: Determine slope

Parallel lines have the same slope. The slope of the line $y = 4x-2$ is $m = 4$.

Step2: Use point - slope form to find equation

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-1,3)$ and $m = 4$, we have $y - 3=4(x+1)$.

Step3: Convert to slope - intercept form

Expand: $y - 3=4x+4$. Then $y=4x + 7$.

9.

Answer:

Step1: Determine slope

The slope of the line $y=\frac{1}{2}x + 1$ is $m_1=\frac{1}{2}$. For a line perpendicular to it, the slope $m_2$ satisfies $m_1m_2=-1$. So $m_2=-2$.

Step2: Use point - slope form to find equation

Using the point $(0,2)$ (which is the y - intercept since $x = 0$) and $m=-2$ in the point - slope form $y - y_1=m(x - x_1)$, we get $y-2=-2(x - 0)$.

Step3: Convert to slope - intercept form

Simplify to get $y=-2x+2$.