Question 42: Which equation represents the line that passes through the points
(-1, -2) and (3, 10)? *
O y = 3x + 1
O y = 3x – 1
O y = 4x + 2
O y = 4x – 2

Next we will be using the point-slope form then convert into slope-intercept form. You can also use the slope-intercept form to substitute one of these points and solve for the y-intercept. However, I will be using the point-slope form instead.

[tex] \large \boxed{y – y_1 = m(x – x_1)}[/tex]

The equation above is in point-slope form. Next we can substitute one of given points. I will choose (-1,-2) to substitute (You can use another point as well since the outcome would be the same.)

[tex] \large{y – ( – 2) = 3(x – ( – 1))}[/tex]

We substitute x1 = -1, m = 3 and y1 = -2. Next, we simplify the equation and convert it in slope-intercept form.

Use the slope formula below (Rise Over Run)

[tex] \large \boxed{m = \frac{y_2 – y_1}{x_2 – x_1} }[/tex]

We are given two points. Substitute those points in the equation. Remember that it is (x,y) and not (y,x).

[tex] \large{m = \frac{10 – ( – 2)}{3 – ( -1)} } \\ \large{m = \frac{10 + 2}{3 + 1} \longrightarrow m = \frac{12}{4} } \\ \large \boxed{\purple{m = 3}}[/tex]

Next we will be using the point-slope form then convert into slope-intercept form. You can also use the slope-intercept form to substitute one of these points and solve for the y-intercept. However, I will be using the point-slope form instead.

[tex] \large \boxed{y – y_1 = m(x – x_1)}[/tex]

The equation above is in point-slope form. Next we can substitute one of given points. I will choose (-1,-2) to substitute (You can use another point as well since the outcome would be the same.)

[tex] \large{y – ( – 2) = 3(x – ( – 1))}[/tex]

We substitute x1 = -1, m = 3 and y1 = -2. Next, we simplify the equation and convert it in slope-intercept form.

[tex] \large{y + 2 = 3(x + 1)} \\ \large{y = 3(x + 1) – 2} \\ \large{y = 3x + 3 – 2} \\ \large \boxed{ \red{y = 3x + 1}}[/tex]

Answery=3x+1Answer:y = 3x + 1

Step-by-step explanation:first we need to find the slope

m = (y2-y1) / (x2-x1)

m = (10 – -2) / (3 – -1) = 3

note that it does not matter which points you chose to be second or first

then use slope point equation again it does not matter which point you use

y – y1 = m ( x – x1 )

y – 10 = 3 ( x – 3)

y – 10 = 3x -9

y = 3x -9 + 10

y = 3x +1