The equation of line gh is y = 4x − 3. write an equation of a line perpendicular to line gh in slope-intercept form that contains point (2, 3). (5 points)

The equation of this line is y = -1/4x - 7/2

Step-by-step explanation:

To find this, we need to first look for the slope. Perpendicular slopes have opposite and reciprocal slopes. Since the original line has a slope of 4, this means the new one has a slope of -1/4.

Given that slope, we can find the equation by starting with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the slope in for m and the two coordinates in for (x1, y1).

y - 3 = -1/4(x - 2)

Now that we have this, solve for y for the slope-intercept form.

y - 3 = -1/4x + 1/2

y = -1/4x + 7/2

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step-by-step explanation:

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region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true