To find the equation of a line when you know its slope and y-intercept, you can use the slope-intercept form, which is expressed as:
y = mx + b
In this equation:
- y represents the dependent variable (the value of y at a given x).
- m is the slope of the line.
- x is the independent variable.
- b is the y-intercept, the point where the line crosses the y-axis.
In your case, the slope (m) is 23 and the y-intercept (b) is 9. Plugging these values into the slope-intercept form, we have:
y = 23x + 9
This means that the equation of the line with a slope of 23 and a y-intercept of 9 is y = 23x + 9. You can use this equation to find the value of y for any given x along the line. For instance, if x is 1, then:
y = 23(1) + 9 = 23 + 9 = 32
So, at x = 1, y would equal 32. Similarly, you can substitute any value for x to find the corresponding value of y. This makes the equation very useful in understanding the relationship between x and y on this linear graph.