Question

To write an equation of the line in slope-intercept form, we need the slope and a point on the line. You've mentioned the slope, but you didn't provide a point. Please provide the point, and I can help you write the equation.

Answer 1

The student provided the slope and y-intercept of a line in a graph as 3 and 9, respectively, therefore, the slope-intercept form of the line's equation is y = 3x + 9.

Step-by-step explanation:

To write the equation of a line in slope-intercept form, which is commonly expressed as y = mx + b, you need two key pieces of information: the slope (m) and the y-intercept (b). The slope represents the rise over run, showcasing how steep the line is. The y-intercept is the point where the line crosses the y-axis. For instance, with a slope of 3, it means for every 1 unit increase in x, y increases by 3 units.

In Figure A1 Slope and the Algebra of Straight Lines, the line graph shows a y-intercept of 9 and a slope of 3. This information allows us to write down the equation of the line as y = 3x + 9. The importance of the slope and y-intercept is that they define the unique characteristics of a straight line on a coordinate plane.