Question

can someone help me understand how to find the slope intercept form in a equation using ( y=mx+b )please n thank you!

Answer 1

y=-1/2+3

Explanation:

first, we have to determine if the slope is positive or negative. if it is going up to the right, it is positive. if it goes up to the left, it is negative. to find the slope, we need two or three points where the x and y values are both whole numbers. for this, we can use the y-intercept (0,3), (-2,4), and (-4,5). we can look at the line and see that from (0,3) to (-2,4) the line rises 1 and runs -2. this supports the claim that the slope is negative. from (-2,4) to (-4,5), the line rises 1 and runs -2. this is the same as the slope from (0,3) to (-2,4), so we can say that it is the slope of the line. since slope is written as rise over run, we can write the slope as -1/2. for the y-intercept, or b, we have to see what y is when x is 0. y is 3, so the y intercept is 3. in y=mx+b, m=slope and b=y intercept, so we plug these values in and we have the graph in slope intercept form.

Answer 2

Slope-intercept form: y = - ½x + 3

Explanation:

In the slope-intercept form, y= mx + b:

m = slope

b = y-coordinate of the y-intercept, (0, b). The y-intercept is the point on the graph where it crosses the y-axis. At that given point, the value of x = 0.

Start by choosing two points from the graph that you could use to solve for the slope of the line. I often use the y-intercept as one of the points.

Use the following points: (0, 3) and (6, 0):

Let (x₁, y₁) = (0, 3) ⇒ This is the y-intercept.

(x₂, y₂) = (6, 0) ⇒ This is the x-intercept, the point on the graph where it crosses the x-axis.

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

`m = (0 - 3)/(6 - 0) = (-3)/(6) = - (1)/(2)`

Hence, the slope of the line is: m = - ½.

As previously mentioned, one of the points we used to solve for the slope is the y-intercept, (0, 3). Its y-coordinate is the value of b = 3 that you will use for the equation.

Therefore, the linear equation in slope-intercept form is: y = - ½x + 3.