Silas claims that the equation y=2+mx, where m is a real number, represents a function whose graph is a straight line.

Mathematics

1 answer:

N76 [4]3 years ago

8 0

Answer:

The claim is true for all values of m.

Step-by-step explanation:

Given

$y = 2 + mx$

Required

Which claim is true [See comment for options]

A linear equation is represented as:

$y = mx + c$

Where

$m = slope$

And the value of m knows no bound

i..e

$m > 0$

$m = 0$

$m < 0$

Hence, (a) is correct

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Why is the equation y-y1=m(x-x1) called the point-slope form?

MatroZZZ [7]

Answer:

The equation of the line with slope m = 2 and passing through the point (1, 1) will be:

$y = 2x$

Step-by-step explanation:

We know that the point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

where

m is the slope of the line

(x₁, y₁) is the point

The formula $y-y_1=m\left(x-x_1\right)$ is termed as the point-slope form of the line equation because if we know one point on a certain line and the slope of that line, then we can easily get the line equation with this formula and, hence, determine all other points on the line.

For example, if we are given the point (1, 1) and slope m = 2

Then substituting the values m = 2 and the point (1, 2)

$y-y_1=m\left(x-x_1\right)$

$y - 2 = 2(x-1)$