Question

use the drawing tools to form the correct answer on the graph. graph the line that represents this equation: y = -5x + 3

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-5x + 3\), when \(x = 0\), \(y=3\). So the line passes through the point \((0,3)\).

Step2: Find another point using the slope

The slope \(m=-5=\frac{-5}{1}\). Starting from the point \((0,3)\), we move down 5 units (because the numerator of the slope is - 5, which represents a decrease in the y - value) and 1 unit to the right (because the denominator of the slope is 1, which represents an increase in the x - value). So from \((0,3)\), moving down 5 units gives \(y = 3-5=-2\) and moving right 1 unit gives \(x=0 + 1 = 1\). So another point on the line is \((1,-2)\).

Step3: Draw the line

Using the two points \((0,3)\) and \((1,-2)\) (or any other points found using the slope - intercept form), we can draw the line. We can also use the line tool to connect the points on the graph.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y=-5x + 3\) passing through the points like \((0,3)\) and \((1,-2)\) (and other points obtained by using the slope) on the coordinate plane.)

Answer:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-5x + 3\), when \(x = 0\), \(y=3\). So the line passes through the point \((0,3)\).

Step2: Find another point using the slope

The slope \(m=-5=\frac{-5}{1}\). Starting from the point \((0,3)\), we move down 5 units (because the numerator of the slope is - 5, which represents a decrease in the y - value) and 1 unit to the right (because the denominator of the slope is 1, which represents an increase in the x - value). So from \((0,3)\), moving down 5 units gives \(y = 3-5=-2\) and moving right 1 unit gives \(x=0 + 1 = 1\). So another point on the line is \((1,-2)\).

Step3: Draw the line

Using the two points \((0,3)\) and \((1,-2)\) (or any other points found using the slope - intercept form), we can draw the line. We can also use the line tool to connect the points on the graph.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y=-5x + 3\) passing through the points like \((0,3)\) and \((1,-2)\) (and other points obtained by using the slope) on the coordinate plane.)