Question

Graph the line that passes through (1, 4), parallel to a line whose slope is -1/4?

Answer 1

To graph a line parallel to one with a slope of -1/4 that passes through (1, 4), find the equation by using the slope-intercept form and the given point to solve for the y-intercept. Plot the y-intercept and use the slope to find a second point, then draw a straight line through both points.

Step-by-step explanation:

To graph a line that passes through the point (1, 4) and is parallel to a line with a slope of -1/4, we start by understanding that parallel lines have identical slopes. Thus, the slope of the line we want to graph will also be -1/4. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

Since we know the slope (m = -1/4) and a point on the line (1, 4), we can substitute these values into the slope-intercept form to find the y-intercept (b). Plugging the values in, we get:

1. 
   
3. 4 = (-1/4)(1) + b
4. 
   
6. 4 = -1/4 + b
7. 
   
9. b = 4 + 1/4
10. 
    
12. b = 4.25

Thus, the equation of our line is y = -1/4x + 4.25. To graph this line, start at the y-intercept (0, 4.25) on the y-axis and use the slope to find another point. Since the slope is -1/4, for every 4 units we move right, we move 1 unit down. Plot the second point accordingly and draw a straight line through these two points, extending the line infinitely in both directions.

Answer 2

The graph is attached.

To graph a line parallel to another line, you can use the fact that parallel lines have the same slope. The given line has a slope of -1/4. Therefore, the line we want to graph also has a slope of -1/4.

The point-slope form of the equation of a line is given by:

`\[ y - y_1 = m(x - x_1) \]`

where:

`\((x_1, y_1)\)` is a point on the line,
`\(m\)` is the slope.

In this case, the point
`\((1, 4)\)` is on the line, and the slope is -1/4. So, the equation of the line in point-slope form is:

`\[ y - 4 = -(1)/(4)(x - 1) \]`

Now, you can simplify this equation to slope-intercept form
`(\(y = mx + b\))` if you prefer. Let's do that:

`\[ y - 4 = -(1)/(4)x + (1)/(4) \]`

Add 4 to both sides:

`\[ y = -(1)/(4)x + (17)/(4) \]`

Now, you can graph this line on a coordinate plane. The slope is negative, indicating that the line slopes downward from left to right. The y-intercept is at
`\(y = (17)/(4)\)`, and the slope is -1/4. Use these details to plot the line on your graph.