Harlen Pritchard

2021-01-04

Given linear equation y = 6 − 7x

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Arham Warner

Skilled2021-01-05Added 102 answers

(a) The linear equation is $y=6-7x$.

In a linear equation $y={b}_{0}+{b}_{1}x$ the constant ${b}_{1}$ be the slope and ${b}_{0}$ be the y-intercept form and $x$ is the independent variable and $y$ is the independent variable.

Comparing the given equation with the general form of linear equation the slope of the equation is –7 and the $y$-intercept is 6.

Thus, the slope of the linear equation is ${b}_{1}=-7$ and the $y$-intercept is ${b}_{0}=6$.

(b) In a linear equation $y={b}_{0}+{b}_{1}x$ the constant ${b}_{1}$be the slope and ${b}_{0}$ be the $y$-intercept form and $x$ is the independent variable and $y$ is the independent variable.

It is known that, the slope of the linear equation $y={b}_{0}+{b}_{1}x$ is upward if ${b}_{1}>0$, the slope of the linear equation $y={b}_{0}+{b}_{1}xy={b}_{0}+{b}_{1}x$ is downward if ${b}_{1}<0$ and the slope of the linear equation $y={b}_{0}+{b}_{1}x$ is horizontal if ${b}_{1}=0.$

Thus, in the given equation $y=6-7x,{b}_{1}=-7<0.$

Thus, the slope is downward.

(c) The linear equation is $y=6-7x$.

Graph the line:

The two points $\left({x}_{1},\hspace{0.17em}{y}_{1}\right)\text{and}\left({x}_{2},\hspace{0.17em}{y}_{2}\right)$ on the given line are obtained:

If $x\hspace{0.17em}=0$,

$y=6+(-7\times 0)$

$y=6$

Thus, one point on the line is $\left({x}_{1},\hspace{0.17em}{y}_{1}\right)=\left(0,6\right).$

If $x\hspace{0.17em}=1$,

$y=6+(-7\times 1)$

$y=-1$

Thus, the second point on the line is $\left({x}_{2},\hspace{0.17em}{y}_{2}\right)=\left(1,-1\right).$

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