# Slope Intercept Form (Definition, Graph & Word Problems)

Slope intercept form is the general form of the straight-line equation. It is represented as:

y=mx+c

Here, c is the y-intercept and m is the slope; hence it is called a slope-intercept form.

The straight-line equation gives the graph of a straight line. They are also called linear equations and consist of simple variables. As we can see in the expression, y = mx+c, x and y are the variables, where x is an independent variable and y is a dependent variable. If we put the values of x, then we can get the respective values of y, and then we plot the graph.

## Slope Intercept Form Definition

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

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

Slope Intercept Form Calculator

## Slope Intercept Form Graph

When we plot the graph for slope intercept from the equation, we get a straight line. Slope-intercept is the best form. Since it is in the form “y=,” it is easy to graph it or solve word problems based on it. We have to put the x-values, and the equation is solved for y.

The best part of the slope-intercept form is that we can get the value of slope and the intercept directly from the equation.

You can easily find slope intercept or equation of straight line using slope intercept form calculator.

## Point Slope-Intercept Form

The point-slope form is also a kind of slope intercept form where the distance between the two points is estimated by drawing a straight line between them. This form is taken from the theory of finding the slope or steepness of a line when two points are given.

The point-slope form formula is given by:

y2,-y1=m(x2-x1)

Therefore, from the above equation, we can derive the slope formula;

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

## Word Problems

Problem 1: Find the straight-line equation that has slope m = 3 and passes through the point (–2, –5).

Solution: By the slope-intercept form, we know;

y=mx+c

Given,

m=3

As per the given point, we have;

y = -5 and x = -2

Hence, putting the values in the above equation, we found;

-5 = 3(-2) + c

-5 = -6+c

c = -5 + 6 = 1

Hence, the required equation will be;

y = 3x+1

Problem 2: Find the straight-line equation that has slope m = -1 and passes through the point (2, -3).

Solution: By the slope-intercept form, we know;

y=mx+c

Given,

m=-1

As per the given point, we have;

y = -3 and x = 2

Hence, putting the values in the above equation, we get;

-3 = -1(2) + c

-3 = -2 + c

c = -3+2 = -1

Hence, the required equation will be;

y = -x-1

## Practice Problems

1. Find the slope of the line y=5x+2
2. Find the intercept of the line y=-2x+9
3. Find the slope of the line which crosses the line at point (-2,6) and have an intercept of 3

## FAQs

How do you find slope intercept form?

In general, the slope intercept form finds the formula: y = mx + b.
M is the slope (lesson on the slope). Mnemonic: ‘m’ means ‘move.’
B is the y-intercept (lesson on the y-intercept). Mnemonic: ‘b’ means where the line begins.

How do you find y MX B?

Use the formula y = mx + b to determine the y-intercept, b. Replace x and y in the formula with the coordinates of one of the presented points, and replace m with the calculated value, (2). Find the line’s equation whose graph contains the points (1,–2) and (6,5).

How do you find the slope of Y MX B?

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the line’s slope and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line passes the y axis.

How do I find slope?

The slope of a line characterizes the direction of a line. To get the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.