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NoblePenguin

Answer:

Our final equation is [tex]\bold{y = \frac{1}{4}x + 3}.[/tex]

Step-by-step explanation:

We are given a coordinate point and the slope of a line. We need to know that:

  • The slope-intercept form of a line is [tex]\text{y = mx + b},[/tex] where m is the slope of the line and b is the y-intercept of the line.
  • The point-slope formula is y - y₁ = m(x - x₁).

We want to end up at the slope-intercept form of the equation. Therefore, we can use the point-slope formula and substitute our values and solve the equation.

[tex]y - 2 = \frac{1}{4}(x - (-4))\\\\y - 2 = \frac{1}{4}x + 1\\\\\small\boxed{\bold{y = \frac{1}{4}x + 3}}[/tex]

Therefore, we have determined that our equation in slope-intercept form is [tex]\bold{y = \frac{1}{4}x + 3}[/tex].

Ben

[tex]\huge\boxed{y=\frac{1}{4}x+3}[/tex]

Hey! Let's start off with the point-slope form equation:

[tex]y-y_1=m(x-x_1)[/tex]

In this equation, [tex]m[/tex] represents the slope and [tex](x_1, y_1)[/tex] is the known point.

Substitute in the values we know:

[tex]y-2=\frac{1}{4}(x-(-4))[/tex]

Subtracting a negative number is the same as adding a positive number.

[tex]y-2=\frac{1}{4}(x+4)[/tex]

Distribute the [tex]\frac{1}{4}[/tex]:

[tex]y-2=\frac{1}{4}x+1[/tex]

Add [tex]2[/tex] to both sides to get the equation in slope-intercept form, which is [tex]y=mx+b[/tex]:

[tex]\boxed{y=\frac{1}{4}x+3}[/tex]

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