Question

If $(2,6)$ and $(-1,-6)$ are two solutions of $f(x)=m x+b$, determine $m$ and $b .$

Name: Problem 83, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2020-07-17T00:09:41-08:00
Duration: 48 s
Channel: Ankit Gupta
Description: If (2,6) and (-1,-6) are two solutions of f(x)=m x+b, determine m and b .

    If $(2,6)$ and $(-1,-6)$ are two solutions of $f(x)=m x+b$, determine $m$ and $b .$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 83

Instant Answer

Solved by Expert Ankit Gupta

07/17/2020

Step 1

Step 1: Write down the equation of the line in slope-intercept form, which is $f(x) = mx + b$. Show more…

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If $(2,6)$ and $(-1,-6)$ are two solutions of $f(x)=m x+b$, determine $m$ and $b .$

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Key Concepts

Y-intercept Determination

The y-intercept is the value of the function when x is zero; it is the point where the graph of the line crosses the y-axis. To find it, one can substitute the coordinates of any known point on the line into the slope-intercept form and solve for the intercept.

Slope Calculation

The slope of a linear function is a measure of its steepness, representing the rate of change of the function with respect to x. It is calculated by dividing the difference in the y-values by the difference in the x-values for any two distinct points on the line.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = m*x + b, where m represents the slope and b represents the y-intercept. This form makes it easy to graph the line by identifying its steepness and the point at which it crosses the y-axis.

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