Write the point-slope form of the equation of the line...

Write the point-slope form of the equation of the line satisfying each of the conditions in Exercises. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Passing through $(-2,-4)$ and $(1,-1)$

Key Concepts

Point-Slope Form

This form of a linear equation is written as y - y? = m(x - x?), where (x?, y?) is a point on the line and m is the slope. It's particularly useful when one point and the slope of the line are known, allowing for a straightforward derivation of the line's equation.

Slope-Intercept Form

This form is written as y = mx + b, with m representing the slope and b representing the y-intercept, the point where the line crosses the y-axis. It's a popular format because it clearly shows how the y-coordinate changes with x and makes graphing the line easier.

Slope Calculation

Slope, denoted as m, measures how steep a line is and is calculated as the ratio of the change in y to the change in x between two points (rise over run). This concept is central to understanding the behavior of linear functions and transitions between different forms of linear equations.

Linear Equations

Linear equations describe straight lines in a coordinate plane and are foundational in algebra. They capture the relationship between variables with a constant rate of change, and their various representations, such as point-slope and slope-intercept forms, provide different advantages depending on the information available.

Transcript

00:01 So in the given question we have to deal with two forms of equations, one of which is the point slop form.

00:11 So here this form represents a line which passes through the point x1 y1 and has a slop equal to m.

00:24 So the equation is y minus y1 is equal to m times x minus x1.

00:31 So this is the point slop form.

00:35 Now next we have the slop intercept form, right? so the slop intercept form represents a line with slop, say, m.

00:56 And if the line cuts the y -axis at b, then we can say that the y -inderset of the line.

01:05 Line is equal to b and such a line is represented by the equation y equals mx plus b which is the slop in the such form so now we have a line that passes through the point minus 2 minus 4 and 1 minus 1 so let's use the point slop form to write an equation for the 9 which passes through say the first point, right? so taking the first point, y minus minus 4 equals m times because this log is unknown, we can take m as the slop, x minus minus 2.

01:59 So this would be y plus 4 equals m times x plus 2.

02:08 So on expanding we would get y plus 4 equals m times x plus 2 times m and y equals m times x plus 2 times m minus 4.

02:25 So let this be equation number one.

02:29 Now let's take the second point which is 1 minus 1 and we know the line passes through this point too.

02:40 So this law according to the point's log form, y minus minus 1 would be equal to m times it's minus 1.

02:51 So this is y plus 1 equals m times m times x minus m so y would be equal to m times x minus 1.

03:08 So let this be equation 2...

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