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 since we don't have the options from Eduphoria, we can't give a final - choice answer.

7.

Step1: Find the 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: Find another point using the slope

The slope $m=-3=\frac{\Delta y}{\Delta x}$. Starting from the point $(0,-1)$, 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 the slope

If a line is parallel to $y = 4x-2$, its slope $m = 4$ (parallel lines have the same slope).

Step2: Use the point - slope form to find the 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 and simplify: $y-3=4x + 4$, so $y=4x+7$. But since we don't have the options from Eduphoria, we can't give a final - choice answer.

9.

Answer:

Step1: Determine the slope

If a line is perpendicular to $y=\frac{1}{2}x + 1$, the slope $m$ of the perpendicular line satisfies $m\times\frac{1}{2}=-1$, so $m=-2$.

Step2: Use the point - slope form to find the equation

Using the point $(0,2)$ and $m=-2$ in the point - slope form $y - y_1=m(x - x_1)$, we have $y - 2=-2(x - 0)$.

Step3: Convert to slope - intercept form

Simplify the equation: $y-2=-2x$, so $y=-2x + 2$. But since we don't have the options from Eduphoria, we can't give a final - choice answer.