To find the equation of the line in slope-intercept form, we first need to calculate the slope of the line using the two given points.
The slope (m) is calculated as:
m = (y2 - y1) / (x2 - x1)
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
Next, we can use one of the given points and the slope to find the y-intercept (b). Since the line passes through the point (1, 3), we can substitute this point into the slope-intercept form of a line (y = mx + b) to solve for b:
3 = 5(1) + b
3 = 5 + b
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
Use the image to answer the question.An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.Use the graph to derive the equation of the line in slope-intercept form.(1 point)
5 answers
Write y−6x=5 in slope-intercept form
To write the equation y - 6x = 5 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we first need to isolate y on one side.
Add 6x to both sides of the equation:
y - 6x + 6x = 6x + 5
y = 6x + 5
Therefore, the equation y - 6x = 5 can be rearranged into slope-intercept form as y = 6x + 5. The slope of the line is 6, and the y-intercept is 5.
Add 6x to both sides of the equation:
y - 6x + 6x = 6x + 5
y = 6x + 5
Therefore, the equation y - 6x = 5 can be rearranged into slope-intercept form as y = 6x + 5. The slope of the line is 6, and the y-intercept is 5.
Describe what makes a proportion. Give an example of a proportion.(2 points)
A proportion is an equation that states that two ratios or fractions are equal. In other words, it shows that two ratios are in balance with each other, maintaining the same relationship.
A proportion can be written in the form a/b = c/d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. In a proportion, the cross products are equal: a * d = b * c.
Example of a proportion:
3/5 = 9/15
In this example, the ratio 3 to 5 is equal to the ratio 9 to 15. This shows that the two ratios are proportional to each other.
A proportion can be written in the form a/b = c/d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. In a proportion, the cross products are equal: a * d = b * c.
Example of a proportion:
3/5 = 9/15
In this example, the ratio 3 to 5 is equal to the ratio 9 to 15. This shows that the two ratios are proportional to each other.