Other Equation of Lines

Slope-Intercept form can be used when given information to find the equation of a line. To use this formula, you will need to know a point, (x1, y1), and the slope of the line, m.

Standard form of a line: Ax + By = CNote both variables are on the same side of the equal sign. A, B and C all represent integers, and A should be positive.

To find an equation of a line:

Generally, you will first need to find the slope, m.

Then use the equation y = mx + b, fill in known information and find b.

Find the equation of the line containing the two points (-3, 4) and (2, 1)

First: find the slope:

Use either of the 2 given points in the slope-intercept formula

y =mx+ b

(1) =(2) + bclear the parentheses

1 = + bclear the fraction, multiply both sides of the equation by 5

5(1) = -6 + 5bSimplify

5 = -6 + 5badd 6 to both sides of the equation

11 = 5bmultiply by 1/5, get b alone

= b

y =x +

Slope-Intercept form – very useful when graphing the line

Start on the y-axis up at 11/5 or 2.2

and from there go down 3 and over to the right 5

Find the equation of the line that satisfies the given conditions and graph the line.

m = 0 ; (-3, -1)

Find the equation of the line that satisfies the given conditions and graph the line.

(5, 2) ; (1, -3)

Point-Slope form can also be used when given information to find the equation of a line.

To use this formula, you will need to know a point, (x1, y1), and the slope of the line, m.

Point-Slope form: y – y1 = m(x – x1)

To find an equation of a line:

You will first need to find or identify the slope, m.

Then use the equation y – y1 = m(x – x1), simplify and solve for y to put the equation into

Slope-Intercept form.

Find the equation of the line containing the slope -3 and passes through the point (-2, 5)

Use the given point and the slope in the Point-Slope formula, y – y1 = m(x – x1)

y – (5) = (-3)(x – (-2))clear the parentheses

y – 5 = -3(x + 2)

y – 5 = -3x – 6 add 5 toboth sides of the equation

y = -3x – 1

Slope-Intercept form – very useful when graphing the line

Start on the y-axis down at -1

and from there go down 3 and over to the right 1

Find the equation of the line that satisfies the given conditions and graph the line.

Passes through (2, 5) and (-4, 2)

Find the equation of the line that satisfies the given conditions and graph the line.

Undefined Slopeand passes through (3, -1)

Parallel lines have the same slope. m1= m2

Therefore y = 3x – 1 is parallel to 3x – y = -7Solve for y: 3x – y = -7

Since y = 3x + 7, the lines are parallel

Find the equation in standard form for each line that satisfies the given conditions.

Parallel to 3x + y = 5 and passes through (2, 1)

Find the equation in standard form for each line that satisfies the given conditions.

Parallel to x-axis and passes through (-1, 3)

Perpendicular lines have the opposite reciprocal slopes.

Therefore y = 2x + 3 is perpendicular to x + 2y = 4Solve for y: x + 2y = 4

Since y = -½ x + 2, the lines are perpendicular

Find the equation in standard form for each line that satisfies the given conditions.

Perpendicular to 3x – y = 4 and passes through the origin.

Perpendicular to 5x – 2y – 4 = 0 and contains (-3, 5)