Respuesta :
Answer:
Option A is correct.
The linear function that has the steepest slope is, [tex]y = -8x+5[/tex]
Explanation:
Slope intercept form: The general formula is, [tex]y =mx+b[/tex] where m is the slope and b is the y-intercept.
Option A:
According to slope intercept form:
Slope is -8
Similarly, for
Option B :
Slope is -2
Option C:
Slope is 7
Option D :
Slope is 6
Steepest slope defined as that is closest to being vertical.
This could be a line that is positive or negative slope respectively.
Therefore, the linear function that has the steepest slope is, [tex]y = -8x+5[/tex]
The equation [tex]\fbox{\bf y =-8x+5}[/tex] has the steepest slope.
Further explanation:
The slope intercept form of a line is as follows:
[tex]y =mx+c[/tex]
Here, [tex]m[/tex] is the slope of the line.
Step 1:
Compare the equation [tex]y =-8x+5[/tex] with slope intercept form of the equation [tex]y=mx+c[/tex] to obtain the value of [tex]m[/tex].
[tex]m=-8[/tex]
Thus, the slope of the line [tex]y =-8x+5[/tex] is [tex]-8[/tex].
Step 2:
The equation [tex]y-9=-2\left({x + 1}\right)[/tex] can be solved as follows:
[tex]\begin{aligned}y-9& =-2\left({x+1}\right)\hfill\\y-9&=-2x-2\hfill\\y&=-2x+7\hfill\\ \end{aligned}[/tex]
Compare the equation [tex]y=-2x+7[/tex] with slope intercept form of the equation [tex]y=mx+c[/tex] to obtain the value of [tex]m[/tex].
[tex]m=-2[/tex]
Thus, the slope of the line [tex]y-9 =-2\left( {x+1}\right)[/tex] is [tex]-2[/tex].
Step 3:
Compare the equation [tex]y=7x-3[/tex] with slope intercept form of the equation [tex]y=mx+c[/tex] to obtain the value of [tex]m[/tex].
[tex]m=7[/tex]
Thus, the slope of the line [tex]y=7x-3[/tex] is [tex]7[/tex].
Step 4:
The equation [tex]y-2=6\left({x+10}\right)[/tex] can be solved as follows:
[tex]\begin{aligned}y-2&=6\left({x + 10}\right)\hfill\\y-2&=6x+60\hfill\\y&=6x+62\hfill\\ \end{aligned}[/tex]
Compare the equation [tex]y=6x+62[/tex] with slope intercept form of the equation [tex]y=mx+c[/tex] to obtain the value of [tex]m[/tex].
[tex]m=6[/tex]
Thus, the slope of the line [tex]y-2=6\left({x+10}\right)[/tex] is 6.
Steepest slope defined as that is closest to being vertical. This could be a line that is positive or negative slope respectively.
From the above equations, it is observed that the equation [tex]y=-8x+5[/tex] has the steepest slope among the all given equation.
Thus, the equation [tex]\fbox{\bf y =-8x+5}[/tex] has the steepest slope.
Learn more:
1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12
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3. what are the domain and range of the function f(x) = 3x + 5?
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Answer Details :
Grade: High School.
Subject: Mathematics.
Chapter: linear equation.
Keywords:
Slope intercept form, slope, steeper, steepest, equation, slope intercept form of the line, steeper slope, equation, function, expression, y=mx+c, y=-8x+5, y=7x-3.
