Write each equation in slope–intercept form. Then find the slope and the y-intercept of the line

Write each equation in slope–intercept form. Then find the...

Key Concepts

Y-Intercept

The y-intercept is the point where the line crosses the y-axis in a coordinate system. In the slope–intercept form of a linear equation, it is indicated by the constant term b, which represents the value of y when x equals zero.

Algebraic Manipulation

Algebraic manipulation refers to the process of rearranging equations using operations such as the distributive property, addition, subtraction, multiplication, and division. This process is crucial when transforming an equation into slope–intercept form to clearly reveal the slope and y-intercept.

Slope-Intercept Form

The slope–intercept form of a line is an algebraic expression written as y = mx + b, where m represents the slope of the line and b represents the y-intercept. Converting an equation to this form makes it easy to identify these key characteristics quickly.

Slope

The slope of a line is a measure of its steepness and direction. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line, and in the slope–intercept form it is represented by the coefficient m.

Transcript

00:01 So for here, my objective is to write the equation in slope intercept form and then to find the slope and y intercept of the line.

00:08 So slope intercept form, remember, is y equals mx plus b, which means that i need to take this equation and manipulate it so that way y is isolated.

00:17 To do that first, i'm going to distribute 5.

00:20 So i would get 10x minus 15y equals 4.

00:25 So now i've got y being multiplied by negative 15 and also being added by 10x.

00:31 Because when i solve i go and reverse pemdas, i'm going to get rid of my 10x first by subtracting it.

00:36 Some people might think you should add because it's minus here, but if it was 10x plus 10x, that would be 20x.

00:42 It wouldn't cancel.

00:43 We wanted to cancel out and become zero.

00:45 And then whatever i do on one side, i have to do on the other.

00:48 So i also have to subtract 10x over here.

00:50 I'm going to bring my equal sign straight down.

00:53 Now, again, it's important to know that this negative we have not dealt with yet.

00:57 We only got rid of my 10x.

00:59 So on the left, we have negative 15y.

01:04 Don't overlook that negative sign.

01:06 On the right, i have 4 minus 10x.

01:08 So i want to subtract those two terms, but i can't actually subtract them because they're not like terms.

01:14 My next step is to get rid of negative 15 by dividing.

01:18 Now, when i divide on the right by negative 15, i want to make sure i draw one big fraction bar to show that i'm dividing both 4 and negative 10x by negative 15.

01:27 So now i've got y by itself.

01:30 I'm going to use a method that i call the beans, but before i do that, because my fraction involves subtraction and a negative, i actually like to do keep change opposite.

01:42 I think it's just going to help maintain our signs so we don't make any errors.

01:47 So i'm going to use this thing i call the beans...

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