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Write the equation of each line in slope-intercept form.

Write the equation of each line in slope-intercept form.-example-1
User Obaylis
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What is the Slope Intercept Form of a Line?

The graph of the linear equation y = mx + c is a line with m as the slope, and m, and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, represents the steepness of a line. The slope of the line is also termed a gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Here, the distance c is called the y-intercept of the given line L.

So, the coordinate of a point where the line L meets the y-axis will be

(0, c). That means line L passes through a fixed point (0, c) with slope m.

We know that, the equation of a line in point-slope form, where (x1, y1) is the point and slope m is:

(y – y1) = m(x – x1)

Here, (x1, y1) = (0, c)

Substituting these values, we get;

y – c = m(x – 0)

y – c = mx

y = mx + c

Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c

Note: The value of c can be positive or negative based on the intercept made on the positive or negative side of the y-axis, respectively

Slope Intercept Form x Intercept

We can write the formula for the slope-intercept form of the equation of line L whose slope is m and x-intercept d as:

y = m(x – d)

Here,

m = Slope of the line

d = x-intercept of the line

Sometimes, the slope of a line may be expressed in terms of tangent angle such as:

m = tan θ

User Ricardo Velhote
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